Ion concentrations models utilizing convenient pH and electrical conductivity measurements

Abstract

The online analysis of industrial process solutions, such as copper sulfate/acid electrolytes, is challenging due to challenges and high costs of real-time characterization methods, highlighting the need for accurate, cost-effective, and rapid-response techniques. This study models the concentrations of key ions [H⁺], [HSO₄⁻], [SO₄²⁻], and [Cu²⁺] using convenient pH and electrical conductivity (EC) measurements in copper sulfate/acid electrolytes. Initial ion concentrations are determined through thermodynamic equilibrium simulations, and data from 100 ambient temperature trials is used to train the models across a wide range of conditions. Two approaches are explored, first a set of direct empirical equations, which effectively estimate ion concentrations but exhibit higher-order errors at certain data points for [Cu²⁺], and second a system of equations method that integrates pH and EC models with equilibrium and mass balance equations, achieving near-perfect precision with at least 97 % confidence. Additionally, the activity coefficient of [H⁺] is modeled. The findings have significant practical applications in electrolyte concentration determination, as well as kinetic and extraction studies in Lewic cell and membrane modules, particularly for copper Pregnant Leach Solution (PLS) with pH values ranging from 1 to 2.4.